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Collar lemma for Hitchin representations

Gye-Seon Lee and Tengren Zhang

Geometry & Topology 21 (2017) 2243–2280

There is a classical result known as the collar lemma for hyperbolic surfaces. A consequence of the collar lemma is that if two closed curves A and B on a closed orientable hyperbolizable surface intersect each other, then there is an explicit lower bound for the length of A in terms of the length of B, which holds for every hyperbolic structure on the surface. In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.

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hyperbolic surfaces, convex real projective surfaces, collar lemma, Hitchin representations
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 30F60, 32G15
Received: 22 December 2015
Revised: 10 July 2016
Accepted: 8 August 2016
Published: 19 May 2017
Proposed: Ian Agol
Seconded: Simon Donaldson, András I. Stipsicz
Gye-Seon Lee
Mathematisches Institut
Ruprecht-Karls-Universität Heidelberg
Im Neuenheimer Feld 205
D-69120 Heidelberg
Tengren Zhang
Mathematics Department
California Institute of Technology
Mail Code 253-37
1200 East California Boulevard
Pasadena, CA 91125
United States